GCSE A2 - Patterns and Sequences

This unit combines skills originally covered by Edexcel's SoW modules:

|||| Unit 2 Module 2-12 of 20

Contents: Patterns and sequences	Time: 3 – 5 hours
SPECIFICATION REFERENCE
A i	Generate integer sequences (including: sequences of odd or even integers, squared integers, powers of 2, powers of 10, triangle numbers)
A i	Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence, or from diagrams
A j	Use linear expressions to describe the nth term of an arithmetic sequence
PRIOR KNOWLEDGE
Know about odd and even numbers Recognise simple number patterns, eg 1, 3, 5, ... Writing simple rules algebraically Raise numbers to positive whole number powers
OBJECTIVES Lesson plans
Find the missing numbers in a number pattern or sequence (7.5, 7.6) Find the nth term of a number sequence as an algebraic expression (7.6) Explain why a number is, or is not, a member of a given sequence (7.6) Produce a sequence of numbers from a given nth term formula (7.6)
DIFFERENTIATION & EXTENSION
Match-stick problems Sequences and nth term formula for triangle numbers, Fibonacci numbers etc Prove a sequence cannot have odd numbers for any values of n Extend to quadratic sequences whose nth term is an2 + bn + c
NOTES
Emphasise the use of appropriate algebraic notation, eg 3n means 3´ n When investigating linear sequences, students should be able to describe the pattern in words, identify the difference between the terms and write the algebraic description of the nth term

Sequences & linear graphs

A2

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Contents: Straight line graphs	Time: 4 – 6 hours
SPECIFICATION REFERENCE
A l	Recognise linear functions from real-life problems and plot their corresponding graphs
A s	Discuss and interpret graphs modelling real-life situations
A m	Interpret information presented in a range of linear graphs
A l	Recognise (when values are given for m and c) that equations of the form y = mx + c correspond to straight-line graphs in the coordinate plane
A l, m	Find the gradient of lines given by equations of the form y = mx + c, when (a) values are given for m and c and (b) the line has been plotted
PRIOR KNOWLEDGE
Experience of plotting points in all quadrants Linear sequences and basic number patterns
OBJECTIVES Lesson plans
Draw linear graphs from tabulated data, including real-world examples (4.1–4.3) Interpret linear graphs, including conversion graphs (4.2–4.3) Interpret graphs in the form y = mx + c (when values for m and c are given) (4.2) Find the gradient and intercept of a straight line graph (4.2)
DIFFERENTIATION & EXTENSION
Plot graphs of the form y = mx + c where students have to generate their own tables and set out their own axes Use a spreadsheet to generate straight-line graphs, posing questions about the gradient of lines Use a graphical calculator or graphical ICT package to draw straight-line graphs Link to scatter graphs and correlation
NOTES
Clear presentation with axes labelled correctly is vital Recognise linear graphs and when data may include incorrect values Link to graphs and relationships in other subject areas, eg science, geography etc Interpret straight line graphs for Functional Elements contexts: o Ready reckoner graphs o Conversion graphs o Fuel bills o Fixed charge (standing charge) and cost per unit Also link conversion graphs to converting metric and imperial units and equivalents (Unit 2)